Divide. Write your answer in simplest form. 2j - 3/5j + 1 ÷ (4j - 1) ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, (2j - 3)/(5j + 1) ÷ (4j - 1) becomes (2j - 3)/(5j + 1) × 1/(4j - 1).Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, (2j - 3)/(5j + 1) × 1/(4j - 1) becomes (2j - 3) / ((5j + 1)(4j - 1)).Simplify denominator: Simplify the denominator by multiplying the two binomials. So, (5j + 1)(4j - 1) = 20j^2 - 4j + 5j - 1.Combine like terms: Combine like terms in the denominator. So, 20j^2 - 4j + 5j - 1 becomes 20j^2 + j - 1.Write in simplest form: Write the answer in the simplest form. So, (2j - 3) / ((5j + 1)(4j - 1)) becomes (2j - 3) / (20j^2 + j - 1).

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Divide. Write your answer in simplest form. $\newline$ $\frac{2j - 3}{5j + 1} \div (4j - 1)$

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Algebra 1

Multiply and divide rational expressions

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Q. Divide. Write your answer in simplest form.

\newline

\frac{2j - 3}{5j + 1} \div (4j - 1)

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, $(2j - 3)/(5j + 1) \div (4j - 1)$ becomes $(2j - 3)/(5j + 1) \times 1/(4j - 1)$ .
Multiply numerators and denominators: Multiply the numerators and then multiply the denominators. So, $(2j - 3)/(5j + 1) \times 1/(4j - 1)$ becomes $(2j - 3) / ((5j + 1)(4j - 1))$ .
Simplify denominator: Simplify the denominator by multiplying the two binomials. So, $(5j + 1)(4j - 1) = 20j^2 - 4j + 5j - 1$ .
Combine like terms: Combine like terms in the denominator. So, $20j^2 - 4j + 5j - 1$ becomes $20j^2 + j - 1$ .
Write in simplest form: Write the answer in the simplest form. So, $(2j - 3) / ((5j + 1)(4j - 1))$ becomes $(2j - 3) / (20j^2 + j - 1)$ .